# Linking Pressure, Force and Velocity

1. Oct 29, 2008

### rickya_23

For a project, i have designed a brief which involves firing paintballs at a target. the paintballs are shot out of a tube which has linked to it a container in which the air pressure (psi) can be altered. it is this pressure that provides the force to propell the paintball towards the target. i have a light gate that will measure the velocity of the paintball as it leaves the tubing, a pressure pump with the ability to alter the psi of the air within the container and a force sensor linked to the target which will register the force of impact.

i want to link the initial pressure within the container (psi) to the force this exerts on the paintball on release of the pressure using an equation. then the force to the velocity of the paintball using an equation.

if anybody can provide equations, help or support it will be much appreciated.
thanks

2. Jul 24, 2009

### geoalfa

3. Jul 27, 2009

### Turv

hi,

This is the way i see it, it may be wrong, but i'll have a go.

Firstly you need to know what velocity pressure is, this is 1/2PV^2, p= density of air 1.2 kg m3. this will give you the velocity pressure in Pascals, convert your Psi into Pascals which is 1 psi = 6.89476 Kpa, your then need to try to find the velocity of your air through tube.

Then i would shoot the paint ball and measure the displacement, then i would use the equation of motion V^2 = U^2 + 2as and work it back to find acceleration, or use S= Ut + 1/2at^2

Force = MxA

Last edited: Jul 27, 2009
4. Jul 27, 2009

### Andy Resnick

The pressure (in psi above air pressure) times the cross-sectional area of the paintball (pi*r^2 and r is measured in inches) gives the force on the ball. In order to calculate the exit velocity of the ball it helps to make some simplifying assumptions (no friction, no air leakage, etc), you need to know how long the tube is, and the mass of the ball. Assuming constant acceleration and a starting velocity of zero gives the final velocity by using one of the kinematic equations from mechanics.

Then, to calculate the imparted force at impact, it again helps to make some simplifications- no air resistance, no spin, etc. But physically, it makes more sense to talk about the energy imparted to the target rather than the force. and again, making some simplifications and using the conservation of energy gives the result.

Does that help?